What is the validity of the prayer of one who performed ablution, and then broke wind after ablution, so she repeated ablution many times, then learned that one afflicted with frequent breaking of wind performs ablution once for each prayer? Is what she did correct? Is it permissible for her to perform ablution once for each prayer? Is it valid for her to perform other prayers with her first ablution as long as it is not invalidated?

The pure Sharia brought ease and removed hardship, and this includes the principle that difficulty brings ease.

So, if flatulence is constant for you most of the time, especially during prayer, then it does not invalidate ablution, because it is considered similar to urinary incontinence. A person with incontinence performs ablution for each prayer after its time has begun, and whatever is released from him thereafter during the prayer does not harm him.

If a person with incontinence performs ablution and prays, and then the next prayer time comes and nothing is released from him, and no other nullifier occurs, is the first ablution sufficient for him? There is a difference of opinion on this, and the correct view within the madhhab is that if nothing is released, then you do not need to perform ablution. However, it is more cautious to perform ablution to avoid the disagreement.